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3 years ago

a gardener plants 36 tomato vines in 2 hours at this rate how many tomato Vines can the gardener plant in 5 hours

Mathematics

1 answer:

Bumek [7]3 years ago

6 0

The Correct Answer is 90

First find out how many in 1 hour so do

36÷2 to get 18

(36 Tomato Vines in 2 Hours)

Then do

18×5 to get 90

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Use the Ratio Test to determine the convergence or divergence of the series. If the Ratio Test is inconclusive, determine the co

jeka57 [31]

Answer:

<h2>A. The series CONVERGES</h2>

Step-by-step explanation:

If $\sum a_n$ is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

$\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho$

If $\rho$ < 1, the series converges absolutely

If $\rho > 1$ , the series diverges

If $\rho = 1$ , the test fails.

Given the series $\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}$

To test for convergence or divergence using ratio test, we will use the condition above.

$a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}$

$\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\$

$\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\$

aₙ₊₁/aₙ =

$\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\$

note that any constant dividing infinity is equal to zero

$|\frac{1+2/\infty+1/\infty^2}{5}|\\\\$

$\frac{1+0+0}{5}\\ = 1/5$

$\rho = 1/5$

Since The limit of the sequence given is less than 1, hence the series converges.

5 0

3 years ago

Explain how to determine which numbers must be excluded from the domain of a rational expression. Please provide an example with

Katarina [22]

Answer:

When we are having a rational expression i.e. a expression of the type:

$\dfrac{f(x)}{g(x)}$

Where f(x) and g(x) are polynomial functions.

Now the domain of this rational expression is whole of the real numbers except the points where the function g(x) will be zero.

Hence we have to exclude the points where the given denominator quantity is zero.

Let us consider an example as:

Let R(x) denote the rational function as:

$R(x)=\dfrac{x^2}{(x-2)(x-3)}$

Now the domain of this rational function will be whole of the real line minus the points where the denominator is zero.

We know that (x-2)(x-3) is zero when x=2 or x=3.

Hence, the domain of R(x) is: R- {2,3}.

7 0

3 years ago

A recipe for 1 batch of muffins included 2/3 cup of raisins. She made 2 1/2 batches of muffins. How many cups of raisins did she

choli [55]

Answer:

If she made <u>2</u> <em>1/2</em> batches of muffins and you had 2/3 of raisins per 1 batch then you'd have a total of 1 2/3 cups of raisins

Step-by-step explanation:

1 batch= 2/3 cups

<u>2 batches</u>=4/3 cups or 1 and 1/3 cups

<em>1/2 batch</em>= 1/2 of 2/3= 1/3 cups

2 batches+1/2 batches= 1 and 1/3 cups+1/3 cups

1 and 1/3 cups+1/3 cups= 1 and 2/3 cups of raisins

3 0

2 years ago

Four gallons of gasoline weigh 25 pounds . find the unit rate in pounds per gallon.

notka56 [123]

There are several information's that are already given in the question. Based on those information's the answer to the question can be easily deduced.
Weight of 4 gallons of gasoline = 25 pounds
Then
Weight of 1 gallon of gasoline = 25/4 pounds
= 6.25 pounds
From the above deduction, we can easily conclude that the unit rate in pounds per gallon of gasoline is 6.25 pounds/gallon. I hope the answer helps you.

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3 years ago

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After the strand of measurement why do you think that graphing and data analysis are easier? Please help ASAP!!! :(

Vikki [24]

It’s organized and you can see it more visually , gives you a way to double check and write down the data properly.

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3 years ago